In recent years, the time variation of Internet traffic has increased due to the growth of streaming and cloud services. Backbone networks must accommodate such traffic without congestion. Traffic engineering with traffic prediction is one approach to stably accommodating time-varying traffic. In this approach, routes are calculated from predicted traffic to avoid congestion, but predictions may include errors that cause congestion. We propose prediction-based traffic engineering that is robust against prediction errors. To achieve robust control, our method uses model predictive control, a process control method based on prediction of system dynamics. Routes are calculated so that future congestion is avoided without sudden route changes. We apply calculated routes for the next time slot, and observe traffic. Using the newly observed traffic, we again predict traffic and re-calculate the routes. Repeating these steps mitigates the impact of prediction errors, because traffic predictions are corrected in each time slot. Through simulations using backbone network traffic traces, we demonstrate that our method can avoid the congestion that the other methods cannot.